Serving the Quantitative Finance Community

 
User avatar
yassin2
Topic Author
Posts: 0
Joined: December 18th, 2002, 1:34 pm

Markovian models

February 24th, 2003, 12:29 pm

what is a markovian model ?is BGM markovian ? if not why ?
 
User avatar
Pat
Posts: 28
Joined: September 30th, 2001, 2:08 am

Markovian models

February 24th, 2003, 2:04 pm

Despite the claims to the contrary, most BGM models are definitely Markovian.A markovian model is one in which, at any pont in time, the entire state of the model is a function of the value of a finite number of "state variables".This is a useful because the value V of most options is also a function of the same state variables.There was a claim (with rigorous proofs seen in some text books) that the only Markovian models are the seperable models of Li, Ritchken, and Sankarsubramanian (pardon me Sankar, I still can't spell your name), but this turns out not to be the case.
 
User avatar
yassin2
Topic Author
Posts: 0
Joined: December 18th, 2002, 1:34 pm

Markovian models

February 24th, 2003, 3:56 pm

so is it possible to write a PDE in BGM approch ? (of options on swap or libor...)
 
User avatar
Pouillot
Posts: 0
Joined: February 17th, 2003, 8:22 am

Markovian models

February 24th, 2003, 4:34 pm

Well, for swaptions in the BGM framework, there is some pretty good approximation available, you can find one in the original paper of Brace-Gatarek-Musiela, and there is also an approximation in a Jamshidian's paper i think . For american style option ( bermuda swaptions ), the dimension of the problem is too high to use the PDE approach properly ( it's unworkable ). So in these case, you use Monte Carlo Methods , you can use Longstaff-Schwarts algorithm or Andersen's.
 
User avatar
VJOHNNY
Posts: 0
Joined: February 24th, 2003, 6:50 pm

Markovian models

February 24th, 2003, 6:55 pm

I am a postgraduate student. I study "MSc RISK MANAGEMENT & FINANCIAL SERVICES", I have some strong educational background in the trading and use of financial derivatives. I need some good idea for a dissertation that will combine financial risk management techniques, with the uses in financial institutions, banks, intermediaries, hedge funds etc.I am particullary interested in the uptodate key sector aspects.